Time Period of Circular Orbit Calculator

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The Two Body Problem

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Circular Orbits

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Circular Orbit Parameters

Geostationary Earth Satellite

✖The Orbit Radius is defined as the distance from the center of the orbit to the orbit's path.ⓘ Orbit Radius [r]

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✖The time period of Orbit is the amount of time a given astronomical object takes to complete one orbit around another object.ⓘ Time Period of Circular Orbit [T_or]

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Formula

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Time Period of Circular Orbit

Formula

`"T"_{"or"} = (2*pi*"r"^(3/2))/(sqrt("[GM.Earth]"))`

Example

`"11261.49s"=(2*pi*("10859km")^(3/2))/(sqrt("[GM.Earth]"))`

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Time Period of Circular Orbit Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time Period of Orbit = (2*pi*Orbit Radius^(3/2))/(sqrt([GM.Earth]))
T_or = (2*pi*r^(3/2))/(sqrt([GM.Earth]))
This formula uses 2 Constants, 1 Functions, 2 Variables

Constants Used

[GM.Earth] - Earth’s Geocentric Gravitational Constant Value Taken As 3.986004418E+14
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Time Period of Orbit - (Measured in Second) - The time period of Orbit is the amount of time a given astronomical object takes to complete one orbit around another object.
Orbit Radius - (Measured in Meter) - The Orbit Radius is defined as the distance from the center of the orbit to the orbit's path.

STEP 1: Convert Input(s) to Base Unit

Orbit Radius: 10859 Kilometer --> 10859000 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_or = (2*pi*r^(3/2))/(sqrt([GM.Earth])) --> (2*pi*10859000^(3/2))/(sqrt([GM.Earth]))

Evaluating ... ...

T_or = 11261.4867499914

STEP 3: Convert Result to Output's Unit

11261.4867499914 Second --> No Conversion Required

FINAL ANSWER

11261.4867499914 ≈ 11261.49 Second <-- Time Period of Orbit

(Calculation completed in 00.004 seconds)

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Created by Karavadiya Divykumar Rasikbhai

Hindustan Institute of Technology and Science (HITS), Chennai, Indian

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< 11 Circular Orbit Parameters Calculators

Orbital Period

Go Time Period of Orbit = 2*pi*sqrt((Orbit Radius^3)/([G.]*Central Body Mass))

Circular Orbital Radius Given Time Period of Circular Orbit

Go Orbit Radius = ((Time Period of Orbit*sqrt([GM.Earth]))/(2*pi))^(2/3)

Speed of Satellite in Circular LEO as Function of Altitude

Go Speed of Satellite = sqrt([GM.Earth]/([Earth-R]+Height of Satellite))

Time Period of Circular Orbit

Go Time Period of Orbit = (2*pi*Orbit Radius^(3/2))/(sqrt([GM.Earth]))

Velocity of Circular Orbit

Go Velocity of Circular Orbit = sqrt([GM.Earth]/Orbit Radius)

Circular Orbital Radius

Go Orbit Radius = Angular Momentum of Circular Orbit^2/[GM.Earth]

Specific Energy of Circular Orbit Given Orbital Radius

Go Specific Energy of Orbit = -([GM.Earth])/(2*Orbit Radius)

Orbital Radius Given Specific Energy of Circular Orbit

Go Orbit Radius = -([GM.Earth])/(2*Specific Energy of Orbit)

Circular Orbital Radius Given Velocity of Circular Orbit

Go Orbit Radius = [GM.Earth]/Velocity of Circular Orbit^2

Specific Energy of Circular Orbit

Go Specific Energy of Orbit = -([GM.Earth]^2)/(2*Angular Momentum of Circular Orbit^2)

Escape Velocity given Speed of Satellite in Circular Orbit

Go Escape Velocity = sqrt(2)*Velocity of Circular Orbit

Time Period of Circular Orbit Formula

Time Period of Orbit = (2*pi*Orbit Radius^(3/2))/(sqrt([GM.Earth]))
T_or = (2*pi*r^(3/2))/(sqrt([GM.Earth]))

What is the shortest orbit time?

The planet with the shortest orbital period (year) is Mercury. The innermost planet in our Solar System completes its elliptical orbit around the Sun once every 87 (Earth) days 21 hours.

How to Calculate Time Period of Circular Orbit?

Time Period of Circular Orbit calculator uses Time Period of Orbit = (2*pi*Orbit Radius^(3/2))/(sqrt([GM.Earth])) to calculate the Time Period of Orbit, The Time Period of Circular Orbit is defined as the amount of time a given astronomical object takes to complete one orbit around another object. Time Period of Orbit is denoted by T_or symbol.

How to calculate Time Period of Circular Orbit using this online calculator? To use this online calculator for Time Period of Circular Orbit, enter Orbit Radius (r) and hit the calculate button. Here is how the Time Period of Circular Orbit calculation can be explained with given input values -> 11261.49 = (2*pi*10859000^(3/2))/(sqrt([GM.Earth])).

FAQ

What is Time Period of Circular Orbit?

The Time Period of Circular Orbit is defined as the amount of time a given astronomical object takes to complete one orbit around another object and is represented as T_or = (2*pi*r^(3/2))/(sqrt([GM.Earth])) or Time Period of Orbit = (2*pi*Orbit Radius^(3/2))/(sqrt([GM.Earth])). The Orbit Radius is defined as the distance from the center of the orbit to the orbit's path.

How to calculate Time Period of Circular Orbit?

The Time Period of Circular Orbit is defined as the amount of time a given astronomical object takes to complete one orbit around another object is calculated using Time Period of Orbit = (2*pi*Orbit Radius^(3/2))/(sqrt([GM.Earth])). To calculate Time Period of Circular Orbit, you need Orbit Radius (r). With our tool, you need to enter the respective value for Orbit Radius and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Time Period of Orbit?

In this formula, Time Period of Orbit uses Orbit Radius. We can use 1 other way(s) to calculate the same, which is/are as follows -

Time Period of Orbit = 2*pi*sqrt((Orbit Radius^3)/([G.]*Central Body Mass))

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